It was columnist Joseph Alsop, if memory serves, who cast his piercing eye on the Middle East in the late 1950s and had this vision: He could have sworn he saw, advancing relentlessly through the Middle East thickets, a "star-spangled boa constrictor with the great, gray head of John Foster Dulles."

Today, you could make that read "the fine, soldierly features of Alexander Haig."

The point now, as it was then, is not that there isn't a threat of Soviet penetration of that turbulent, tormented region. The point is that the Reagan administration, in its nearly limitless zeal to turn back clocks, may well be in danger of repeating history by enveloping its best Middle East friends with a smothering, perhaps crippling, embrace.

In the 1950s (and in some cases on into the 1960s), the lavish, intense, high-visibility American approach -- complete with heavy military aid, formal defense arrangements and base agreements -- did work for a time. But it can also be argued that, in the end, it contributed to the collapse of the celebrated Baghdad Pact, with the fall of the linchpin, pro-Western government of Nuri Said in Iraq. Some would make the same argument in the case of the shah of Iran.

Nothing, in those days, was too much for Nuri or the shah. Or for Lebanon, rescued from disintegration in 1958 with American troops and diplomatic medication, only to come asunder later on. Only Jordan's canny King Hussein survived, among those (Israel aside) who were the center of the most intense U.S. concern.

What brings all this to mind is the first real glimpse of the thrust and emphasis of the Haig-Reagan policy for the Middle East. The recent visit of Israeli Foreign Minister Yitzhak Shamir did wonders to sharpen the focus. Shamir pushed hard for an American commitment to move quickly on the Palestinian issue. Israel's political preoccupation with its forthcoming election at midyear, he argued, is no reason not to revive the suspended West Bank "autonomy" talks.

"We believe it is dangerous to leave the scene of the Middle East without a constant activity in trying to enforce and continue the peace process," he warned publicly. But what he was told by the administration was that "they don't want to continue the ways of the former administration and, in their view, they have more urgent priorities."

While Shamir did not elaborate out loud, other officials leave no question about the "priorities" the Reagan administration has in mind for the Mideast: aThe big concern is not Arab/Israeli but East/West. The line that Haig is reportedly giving to visitors is that the "Soviets are on the move, that the whole [Persian] Gulf will fall within a year or two if the United States does not make some countermoves."

This fits comfortably into the Reagan administration's larger world view, whether we're talking about Saudi Arabia or El Salvador. The early emphasis, across the board, has been on military buildups and an expanded American military presence almost anywhere and everywhere to meet the global Soviet/communist challenge.

The question is how you apply this grand strategic concept, specifically and effectively, in the Middle East. The Carter administration made a modes start -- with an enlarged naval presence in the Persian Guld; with agreements to "preposition" military supplies and acquire emergency access to military "facilities" (we don't say "bases") in the area; and with the assembly of the beginnings of a mobile Rapid Deployment Force.

That, Carter's people thought, was about as much as the market could bear, boa constrictor-wise.

And right there is the Haig/Reagan difference. The new administration is convicted that it can capitalize on the common security concerns of three seemingly improbable collaborators -- Israel, Egypt and Saudi Arabia.The hope is that all there can be made to see the same Soviet threat that the administration sees. The further hope, which many observers think is unrealistic, is that they will be sympathetic to U.S. security concerns even while nothing much is being done about their interests in the unfinished business of the Camp David framework for Arab-Israeli peace.

Economic aid would be the incentive to President Anwar Sadat to provide for a more substantial American military presence on Egyptian bases. More arms for Israel, on more generous financial terms, would be the trade-off for upgrading the range and firepower of Saudi F15s with the bomb racks, fuel tanks and missiles Carter refused to provide. The Reagan policymakers, it's reliably reported, dream on about the real possibility of some sort of permanent deployment of ground forces on Sinai bases soon to be turned back to Egypt or in Israel itself -- even while both Israel and Egypt, each for its own reasons, keep right on insisting the idea is politically and diplomatically unbearable.

You can't rule out a change of heart. But anything in the way of a Mideast military presence as star-spangled as the Reagan administration seems to have in mind more demonstratable evidence of an immediate Soviet threat.